A two-level method in time and space for solving the Navier–Stokes equations based on Newton iteration

A two-level method in time and space for solving the time-dependent Navier–Stokes equations based on Newton iteration is considered in this paper. Considering that the small eddy components carry little part of the whole energy, we use a larger time step size to obtain the small eddy component, as compared with the large eddy components. Numerical analysis shows that it is possible to choose a proper time step size without compromising the overall accuracy. Moreover, some numerical examples are provided to complement our theoretical analysis.